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Flag-Transitive 6-(v, k, 2) Designs
Department of Mathematics, Hunan University of Humanities Science and Technology, Loudi, China
Department of Mathematics, Changshu Institute of Technology, Changshu, China
Department of Mathematics, Hunan University of Humanities Science and Technology, Loudi, China
- 1 Department of Mathematics, Hunan University of Humanities Science and Technology, Loudi, China
- 2 Department of Mathematics, Changshu Institute of Technology, Changshu, China
- 3 Department of Mathematics, Hunan University of Humanities Science and Technology, Loudi, China
Advances in Pure Mathematics·Volume 04 (2014)·Pages 203–208·Published 5 May 2014·DOI10.4236/apm.2014.45026
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Abstract
The automorphism group of a flag-transitive 6–(v, k, 2) design is a 3-homogeneous permutation group. Therefore, using the classification theorem of 3–homogeneous permutation groups, the classification of flag-transitive 6-(v, k,2) designs can be discussed. In this paper, by analyzing the combination quantity relation of 6–(v, k, 2) design and the characteristics of 3-homogeneous permutation groups, it is proved that: there are no 6–(v, k, 2) designs D admitting a flag transitive group G ≤ Aut (D) of automorphisms.
KeywordsFlag-TransitiveCombinatorial DesignPermutation GroupAffine Group3-Homogeneous Permutation Groups
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